Models of bus queueing at curbside stops

We consider curbside bus stops of the kind that serve multiple bus routes and that are isolated from the effects of traffic signals and other stops. A Markov chain embedded in the bus queueing process is used to develop steady-state queueing models of this stop type, as illustrated by two special cases. The models estimate the maximum number of buses that can arrive at and serve a stop and still satisfy a specified target of average bus delay. These models can be used to determine, for example, a stop's suitable number of bus berths, given the bus demand and the specified delay target. The solutions for the two cases are used to derive a closed-form, parsimonious approximation model for general cases. This approximation matches simulations reasonably well for many conditions that arise in real settings; differences of less than 10% were common. Our results unveil how suitable choices for the number of bus berths are influenced by both the variation in the time that buses spend serving passengers at the stop and the specified delay target. The models further show why the proxy measure commonly used for the delay target in previous bus stop studies is a poor one.